Paper bags used by grocery stores and take-out restaurants are now recyclable. This is awesome. However, the best thing for the environment is to use reusable bags when at all possible.
Clean kraft paper bags that are 100% paper are recyclable and should be bundled with cardboard or placed in Blue Bag #1 along with other paper products. Soiled paper bags go into compost. Paper bags may also be used as a mini bin liner to gather household organics. Please note that many bags used for food products (such as flour, sugar) have a moisture-resistant barrier to keep products stable, and those are compost. Bags containing plastics are waste.